As Brion's post implied, staying design is not a "yes or no" thing, it's a "depends" thing. I'm not a rigger, but I wouldn't give much credence to anyone who would tell you "yes" or "no" on adding backstays without seeing your boat, researching the original rigging plan, determining your intended use (i.e. day-sailing, coastal cruising, racing, offshore passagemaking), etc. Not much help, I know.
On the other hand, you could just add them and see what happens...
if it were me, though, I'd probably look out on the web for any Gulfstar 44 owners that complain about their mizzens falling down before I'd spend a whole bunch of time, energy and money...
Todd Anderson
S/V Earendil